In [1]}, Bhatt and Scholze introduce the pro-étale site for schemes and perfectoid spaces. We review the definition here.

A map \(f:Y=(S,S^+)\rightarrow X=(R,R^+)\)  of affinoid perfectoid spaces is called affinoid pro-étale if it can be written as a cofiltered limit of étale maps \(Y_i = (S_i,S_i^+)\rightarrow X\)  of affinoid perfectoid spaces. More generally, a map \(f:Y\rightarrow X\)  of perfectoid spaces is pro-étale if is locally on the source and target affinoid pro-étale.
